ieee journal on selected areas in communications, … · 2018-05-17 · ieee journal on selected...

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 31, NO. 9, SEPTEMBER 2013 1889

Distributed Network SecrecyJemin Lee, Member, IEEE, Andrea Conti, Senior Member, IEEE, Alberto Rabbachin, Member, IEEE, and

Moe Z. Win, Fellow, IEEE

Abstract—Secrecy is essential for a variety of emerging wirelessapplications where distributed confidential information is com-municated in a multilevel network from sources to destinations.Network secrecy can be accomplished by exploiting the intrinsicproperties of multilevel wireless networks (MWNs). This paperintroduces the concept of distributed network secrecy (DNS) anddevelops a framework for the design and analysis of secure,reliable, and efficient MWNs. Our framework accounts for nodespatial distribution, multilevel cluster formation, propagationmedium, communication protocol, and energy consumption. Thisresearch provides a foundation for DNS and offers a new per-spective on the relationship between DNS and network lifetime.

Index Terms—Distributed network secrecy, self-organizingwireless networks, stochastic geometry, energy consumption,fading channels, performance evaluation.

I. INTRODUCTION

NETWORK SECRECY is a key enabler for various ap-plications in which wireless nodes communicate confi-

dential information to monitoring units (monitors). Exampleapplications include industrial logistics, blue force tracking,and vital-sign acquisition. Confidential information is gen-erally gathered by scattered sensors and communicated tomonitors via hierarchical networking, forming a multilevelwireless network (MWN).

In many applications where sensors are equipped with alimited energy supply (e.g., a battery), its efficient utilizationis needed to increase the network lifetime. Typically, thisis accomplished via self-organization of nodes into clustersat each level [1]–[5]. In this context, the communicationconfidentiality relies on distributed network secrecy (DNS),which accounts for confidentiality of all active links in theself-organizing MWN.

Contemporary wireless security systems, based on crypto-graphic primitives, generally ignore the spatial distribution ofnodes and the physical properties of wireless environments.This conventional approach can be complemented at the

Manuscript received September 15, 2012; revised March 10, 2013. Thisresearch was supported, in part, by the National Science Foundation underGrant CCF-1116501, by MIT Institute for Soldier Nanotechnologies, bythe FP7 European project CONCERTO (Grant Agreement 288502), by theEuropean Commission Marie Curie International Outgoing Fellowship underGrant 2010-272923, and by Korean National Research Foundation underGrants NRF-2011-220-D00076 and NRF-2011-357-D00167. The material inthis paper was presented, in part, at the IEEE International Conference onCommunications, Budapest, Hungary, June 2013.

J. Lee, A. Rabbachin, and M. Z. Win are with the Massachusetts Instituteof Technology (MIT), 77 Massachusetts Avenue, Cambridge, MA 02139 USA(e-mail: [email protected], [email protected], [email protected]).

A. Conti is with the University of Ferrara, Via Saragat 1, 44122 Ferrara,ITALY (e-mail: [email protected]).

Digital Object Identifier 10.1109/JSAC.2013.130920.

physical layer by exploiting intrinsic properties of a wirelessnetwork such as channel and node characteristics [6]–[10].

In the context of physical-layer security, the secrecy ca-pacity has been studied considering fading [11]–[13], mul-tiple access [14]–[16], interference or artificial noise [17]–[19], eavesdropping collusion [20]–[22], and point-to-pointdiversity communications [23]–[25]. Secret-key generation atthe physical-layer using common sources, such as reciprocalwireless channels, has been investigated in [26]–[30]. Inaddition, secrecy in clustered or multi-hop networks has beeninvestigated in [31]–[33]. However, most of these works ignorethe spatial distributions of legitimate and eavesdropping nodes,and relative node positions are important for network secrecy.

A widely used model to represent the node spatial dis-tribution in wireless networks is the Poisson point process(PPP) [34]–[47]. The PPPs have been used to analyze theconnectivity of wireless networks with secrecy [48]–[50].Recently, it has been shown that network interference canbenefit network secrecy [51], [52]. However, DNS of self-organizing MWNs has not been established yet, impeding thedesign of networks capable of offering both communicationconfidentiality and energy efficiency.

We envision a scenario involving a legitimate self-organizing MWN and an eavesdropping MWN. The formeris composed of spatially distributed legitimate nodes aimingto confidentially and efficiently communicate information to amonitor. The latter is composed of spatially distributed eaves-dropping nodes aiming to intercept the information flowingin the legitimate network. We introduce the concept of DNSfor MWNs and define a new performance metric, namelythe DNS throughput, to determine the confidential throughputof MWNs. Starting from the observation that the networkconfiguration optimal for DNS may not be the best for energyefficiency, we characterize the relationship between DNS andnetwork lifetime. This enables us to determine the role ofmultilevel network configuration on secrecy and lifetime, aswell as to establish energy-efficient MWNs with DNS.

In this paper, we provide a foundation for DNS in a varietyof MWN configurations. The key contributions of the papercan be summarized as follows:

• we introduce the DNS concept and define the DNSthroughput in scenarios composed of multilevel legiti-mate network and eavesdropping network;

• we develop a framework, for the design and analysisof wireless networks with DNS, that accounts for nodespatial distribution, multilevel cluster formation, prop-agation medium, communication protocol, and energyconsumption;

• we quantify the DNS throughput and characterize the

0733-8716/13/$31.00 c© 2013 IEEE

1890 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 31, NO. 9, SEPTEMBER 2013

relationship between DNS and network lifetime in self-organizing MWNs.

This work embraces stochastic geometry, probability theory,and communication theory to assess the DNS and the networklifetime for a variety of MWN configurations.

The remainder of this paper is organized as follows: Sec. IIdescribes the network configuration and provides the statisticalcharacterization of received signal-to-noise ratios (SNRs). Sec-tion III introduces the DNS concept and Sec. IV analyzes theDNS in fading channels. Section V presents a case study andquantifies DNS performance. Finally, conclusions are given inSec. VI.

Notation: The notation used throughout the paper is re-ported in Table I.

II. MULTILEVEL WIRELESS NETWORKS

In this section, we describe the legitimate and eavesdrop-ping network configurations, provide the statistical character-ization of the received SNRs, and derive the network lifetimefor an MWN.

A. Multilevel Network Configuration

We consider a scenario composed of a legitimate MWNfor gathering and communicating spatiotemporal informationas well as an eavesdropping MWN aiming to intercept suchinformation. Legitimate and eavesdropping nodes are ran-domly scattered in space according to homogeneous PPPsΠ�, Πe ∈ �

d with spatial densities λ� and λe, respectively.The goal of legitimate nodes is to communicate their observeddata confidentially to monitors. We refer to the entire operationof information gathering via scattered sensors, transmissionthrough MWN, and reception at a monitor as a round.1 Ineach round, legitimate nodes self-organize themselves in anMWN: a node is assigned to a level l with probability β(l)

for l = L,L− 1, · · · , 1 where∑L

l=1 β(l) = 1. Therefore, the

position of nodes in a level l changes from round to round.The self-organizing MWN can be seen as a hierarchical

network with multiple levels (see, e.g., Fig. 1). In each levell = L,L − 1, · · · , 1, the legitimate and the eavesdroppingnetworks are defined as follows:

1) The lth-level legitimate network is composed of nodesthat collect and process the information sent by nodesin level l+1 ≤ L, and transmit them together with theirobserved information to some nodes in level l−1 (mon-itors are in level 0). By the thinning property [53], thedistribution of nodes in level l follows a homogeneousPPP Π

(l)� with spatial density λ

(l)� = β(l)λ� such that∑L

l=1 λ(l)� = λ�.

2) The lth-level eavesdropping network is composed ofnon-colluding eavesdropping nodes, which attempt tointercept the information transmitted from legitimatenodes in level l. The distribution of eavesdropping nodesin level l follows a homogeneous PPP Π

(l)e with spatial

density λ(l)e such that

∑Ll=1 λ

(l)e = λe.

1The monitored environment and the node distribution in a network areconsidered invariant within a round.

TABLE INOTATIONS USED THROUGHOUT THE PAPER

Notation Definition

Π� PPP for legitimate node distribution

Πe PPP for eavesdropping node distribution

λ(l)� Spatial density of legitimate nodes in level l

λ(l)e Spatial density of eavesdropping nodes in level l

L Number of network levels

β(l) Probability for a legitimate node to be in level l

T Symbol time [sec]

W Communication bandwidth [Hz]

N0 One-sided power spectral density of AWGN

α Pathloss exponent

Dx,Y Distance between node positions at x and Y

hx,Y Fading level in the link between node positions x and Y

rl Radius of supporting area (cluster) of a node in level l − 1

bg Generated bits per node in a round

bs Secret bits per node in a round

sl Average number of transmitted symbols/round/node in level l

R� Data rate

Rs Secrecy rate

Echarged Fully-charged energy of node battery

E(l)b Average transmitted energy/bit/node in level l

Δl Energy ratio E(l)b /E

(L)b

ζ(l)� Received SNR by a legitimate node in level l− 1

ζ(l)e Received SNR by an eavesdropping node in level l

ζ� Required SNR at a legitimate receiver

ζe Required SNR at an eavesdropper

V Complement of an event V

V Complement of a set VBX(r) Ball in �d of radius r centered at X

B (r) Volume of BX(r)

E {·} Statistical expectation

P {·} Probability

Fμ(·) Complementary cumulative distribution function of μ

ϑ1 ∧ ϑ2 Conjunction of events ϑ1 and ϑ2

p(l)t Probability of transmission at level l

p(l)c Probability of not having collision at level l

p(l)r Probability of successful reception at level l

p(l)e Probability of unsuccessful eavesdropping at level l

Nround Average number of rounds per node during its lifetime

ρds DNS throughput

Remark 1: The above network configuration representsscenarios in which eavesdropping nodes are organized inmultiple layers (e.g., due to limited intercepting capabilities).However, our framework can be easily adapted to the casewhere all eavesdropping nodes aim to intercept legitimatetransmissions at each level.

After self-organization, the information flows within theMWN as follows. Each node in level l associates with a nodein level l−1 to form clusters. Each cluster consists of all nodesin level l associated with the same node, referred to as gatewaynode (GN), in level l−1. Nodes in a cluster communicate their

LEE et al.: DISTRIBUTED NETWORK SECRECY 1891

Level LLevel L− 1

Level 1 Level 0

Fig. 1. An example of a legitimate MWN with L levels in the presence of an eavesdropping network (circles are legitimate nodes and crosses are eavesdroppingnodes).

observed data to the GN, chosen according to the followingprobabilistic association rule (PAR). For a node in level l atx, all nodes in level l − 1 within the ball Bx(rl) ∈ �

d ofradius rl centered at x, with volume B (rl) = |Bx(rl) |, canpotentially serve as a GN. Thus Gl−1 (x) = Π

(l−1)� ∩Bx(rl) is

the random set of all potential GNs for a node in level l at x.2

If |Gl−1 (x)| �= 0, a GN is selected with equal probability fromGl−1 (x) and is represented by the random variable G (x).3 If|Gl−1 (x)| = 0, there is no GN and data collected by a nodein level l at x will be lost.

Legitimate transmitters do not have channel knowledgeof legitimate and eavesdropping links. Nodes at differentlevels communicate using different resources (e.g., differentfrequency bands or time slots) to avoid inter-level interference,while nodes belonging to the same level share the communi-cation resources according to an intra-level medium accesscontrol (MAC) protocol.4

We now give a lemma for the derivation of DNS and energyconsumption.

Lemma 1: For two independent homogeneous PPPsΠu, Πv ∈ �

d with densities λu and λv, respectively, thefollowing property holds

EΠu,Πv

{ ∑X∈Πu∩A

g(X,Πv)

}=λu

∫AEΠv{g(ω,Πv)} dω

(1)

where A is a bounded space with volume |A|. When theprocess g(ω,Πv) is stationary in ω ∈ �d, (1) leads to

EΠu,Πv

{ ∑X∈Πu∩A

g(X,Πv)

}= λu |A| p (2)

where

p = EΠv{g(ω,Πv)} . (3)

2For example, rl corresponds to the maximum distance that makes anaverage SNR not less than a minimum required value, depending on thereceiver sensitivity and communication reliability.

3The probabilistic behavior of G (x) depends on Π(l−1)� process according

to the PAR.4Our framework is valid for various MAC protocols. An example of MAC

protocol will be presented in Sec. V.

Proof: The left side of (1) can be written as

EΠu,Πv

{ ∑X∈Πu∩A

g(X,Πv)

}(4)

= EΠv

{EΠu

{ ∑X∈Πu

�A(X) g(X,Πv)

}}

(a)= EΠv

{∫Ag(ω,Πv)μu(dω)

}(b)= λu EΠv

{∫Ag(ω,Πv)

}dω

(c)= λu

∫AEΠv{g(ω,Πv)} dω

where μu(dω) is the average number of nodes in dω and

�A(ω) �{1, if ω ∈ A0, otherwise .

(5)

In (4), (a) is from the Campbell’s theorem [53], (b)holds for a homogeneous PPP, and (c) is true for finiteEΠv

{∫A |g (ω,Πv) |dω

}. When the process g(ω,Πv) is sta-

tionary, we have

λu

∫AEΠv{g(ω,Πv)} dω = λu |A| p

where p is given by (3).We now obtain the spatial density of nodes in a cluster

according to the aforementioned PAR.Lemma 2 (Node density in a typical cluster): The spatial

density of nodes in a typical lth-level cluster is

λ(l)c = p(l)ga λ

(l)� (6)

where p(l)ga is the probability of gateway association given by

p(l)ga =1− exp

{−λ

(l−1)� B(rl)

}λ(l−1)� B(rl)

. (7)


Proof: The average number of nodes at level l associatedwith a typical GN at the origin o is given by

EΠ

(l)� ,Π

(l−1)�

⎧⎪⎨⎪⎩

∑X∈Π

(l)� ∩Bo(rl)

�Pl−1(o)(X)

⎫⎪⎬⎪⎭ (8)

where Pl−1(y) = {x ∈ By(rl) : G(x) = y} is the randomset of all potential positions where nodes in level l associatewith the GN in level l − 1 at y. The probabilistic behaviorof Pl−1(y) depends on Π

(l−1)� . Using Lemma 1 with Πu =

Π(l)� , Πv = Π

(l−1)� , λu = λ

(l)� , and A = Bo(rl), we have

EΠ

(l)� ,Π

(l−1)�

⎧⎪⎨⎪⎩

∑X∈Π

(l)� ∩Bo(rl)

�Pl−1(o)(X)

⎫⎪⎬⎪⎭ = λ

(l)� B(rl) p

(l)ga

(9)

where

p(l)ga = P {x ∈ Pl−1(o)} x ∈ Bo(rl) (10)

is the probability that a node in level l, within the radius rlfrom the typical GN, associates with the typical GN. Usingthe total probability theorem, (10) becomes

p(l)ga =∞∑

n=0

1

n+ 1

(λ(l−1)� B(rl)

)nn!

exp{−λ

(l−1)� B(rl)

}(11)

which results in (7). Dividing (9) by B(rl) gives the spatialdensity of nodes in a typical lth-level cluster as (6).

B. Signal-to-Noise Ratio Characterization

The instantaneous SNR per symbol received by a node atY ∈ Πv from a node in level l at x is given by5

ζ(l)v =E

(l)b R� G0 |Hx,Y|2

N0WD−α

x,Y (12)

where E(l)b is the average transmitted energy per bit from a

node at level l; N0 is the one-sided power spectral density(PSD) of the additive white Gaussian noise (AWGN); R� isthe data rate (R�T bits transmitted in a symbol duration T ); Wis the transmission bandwidth; G0 is a constant that dependson the antenna gains and the wavelength; Dx,Y = ‖x−Y‖is the distance between the transmitter and receiver; Hx,Y isthe fading level of the link; and α is the pathloss exponent.

We now determine the complementary cumulative distribu-tion function (CCDF) of the received SNR.

Lemma 3 (CCDF of the received SNR in generic fading):The CCDF of the SNR received by a node at Y ∈ Πv froma node in level l at x is given by

Fζ(l)v(ξ) =

1

2+

∫ ∞

0

Im

{φ|Hx,Y|2(jω)φDα

x,Y

(−jω ξN0W

E(l)b R�G0

)}πω

dω (13)

5For a legitimate receiver Πv = Π(l−1)� and for an eavesdropper Πv =

Π(l)e . For notational brevity, we suppress the dependence of ζ

(l)v on x and

Y.

where φV (jω) is the characteristic function (CF) of the randomvariable V . The CF of Dα

x,Y is given by

φDαx,Y

(jω) =2 (−jω)−2/α

αr2lγ

(2

α,−jω rαl

)(14)

where γ(· , ·) is the lower incomplete Gamma function [54].Proof: The CCDF of the received SNR in (12) condi-

tioned on D, is equal to6

P

{ζ(l)v > ξ |D

}= FU(0)

where U = |H|2 − N0W

E(l)b R�G0

Dαξ. The CF of U is given by

φU(jω) = φ|H|2(jω) e−jω

ξN0WDα

E(l)b R�G0 .

By using the inversion theorem,7 the conditional CCDF of thereceived SNR results in

Fζ(l)v |D(ξ)=

1

2+

∫ ∞

0

Im

{e−jω

ξN0WDα

E(l)b R�G0 φ|H|2(jω)

}

π ωdω.

(15)

It can be shown that D2 follows a uniform distribution inthe interval

(0, r2l

]. Therefore, for a random distance D, the

CCDF in (15) is now given by (13) where

φDα(jω) =2

r2l

∫ rl

0

ξejωξαdξ

which results in (14).

C. Multilevel Network Lifetime

Nodes in the network drain the battery energy due tomultiple modes of operations such as transmitting, receiving,listening, and processing [56]. Compared to other modes,transmitting mode usually dominates the energy consumptionand thus the node’s lifetime. We now determine the averageenergy consumption per node per round and the networklifetime based on the energy consumption of all transmit-ting nodes.8 In each round, every node generates bg bitsto communicate the observed physical quantity. A node inlevel L communicates bg bits to its GN and a node in levell = L−1, L−2, · · · , 1 communicates its own bg bits togetherwith those successfully collected from nodes in level l+1. Thetotal number of bits communicated by a node in level l at xis then mapped into sl(x) symbols according to the signalingconstellation.

Lemma 4 (Average energy consumption): The average en-ergy consumption per node in a round is given by

Eround = E(L)b R�T

L∑l=1

Δl sl β(l) p

(l)t (16)

6For simplicity, we use D and |H|2 instead of Dx,Y and∣∣Hx,Y

∣∣2.7For a random variable X, the inversion theorem provides [55]

FU(u) =1

2+

1

π

∫ ∞

0

Im{e−jωuφu(jω)

}ω

dω .

8Note that energy consumption of other modes can be included in theevaluation of the nodes’ lifetime (see e.g., [5], [57]).


where, in a level l, Δl is the transmission energy ratio sothat E

(l)b = Δl E

(L)b , sl is the average number of symbols

transmitted by a node per round, given by

sl = E∪Lk=l+1Π

(k)�

{sl(x)} (17)

and p(l)t is the transmission probability of a node, given by

p(l)t = 1− exp

{−λ

(l−1)� B (rl)

}. (18)

Proof: Consider legitimate nodes of an MWN in abounded space A ⊂ �

d, which is a Borel set of �d withvolume |A| � B(rl) for all l. The average energy consump-tion per node per round is given by

Eround

=R�T

λ� |A|EΠ�

⎧⎪⎨⎪⎩

L∑l=1

∑X∈Π

(l)� ∩A

�Tl−1(X) sl(X)E

(l)b

⎫⎪⎬⎪⎭

=R�T

λ� |A|

L∑l=1

E∪Lk=l−1Π

(k)�

⎧⎪⎨⎪⎩

∑X∈Π

(l)�

∩A

�Tl−1(X) sl(X)E

(l)b

⎫⎪⎬⎪⎭

(19)

where

Tl−1 ={x ∈ R

d : |Gl−1 (x) | �= 0}

(20)

is the random set of all positions, where nodes in level ltransmit to GNs in level l − 1. Since Tl−1 depends only onΠ

(l−1)� and sl(x) depends only on Π

(l+1)� ,Π

(l+2)� . . . ,Π

(L)� ,

we can rewrite (19) as

Eround =E

(L)b R�T

λ� |A|

L∑l=1

ΔlslEΠ(l)�

,Π(l−1)�

⎧⎪⎨⎪⎩

∑X∈Π

(l)�

∩A

�Tl−1(X)

⎫⎪⎬⎪⎭

(21)

where sl is given by (17). Using Lemma 1 with Πu = Π(l)� ,

Πv = Π(l−1)� , λu = λ

(l)� , we have

EΠ

(l)� ,Π

(l−1)�

⎧⎪⎨⎪⎩

∑X∈Π

(l)� ∩A

�Tl−1(X)

⎫⎪⎬⎪⎭=λ�|A|β(l) p

(l)t (22)

where

p(l)t = P {x ∈ Tl−1}

is the probability that a node in level l has a GN in level l−1,which results in (18). By substituting (22) into (21), we obtain(16).

The network lifetime is defined as the average number ofrounds, Nround, that a node can operate during its life. It isgiven by

Nround =Echarged

Eround(23)

where Echarged is the fully-charged energy of node battery.Using Lemma 4, Nround becomes

Nround =Echarged

E(L)b R�T

∑Ll=1 Δl sl β(l) p

(l)t

. (24)

III. DISTRIBUTED NETWORK SECRECY CONCEPT

The secrecy of a self-organizing MWN is affected bythe spatial distribution of nodes, the type of communicationprotocols, the quality of all legitimate links, and the capabilityof eavesdropping networks. We now define a new metric forMWNs based on inter-level network secrecy and DNS.

Definition 1 (Inter-level network secrecy): The inter-levelcommunication from a node in level k at x to its GN in levelk−1 achieves network secrecy when the following event S(k)x

is true

S(k)x = T(k)x ∧ C

(k)

x ∧R(k)x ∧ E

(k)

x (25)

where the events T(k)x , C(k)

x , R(k)x , and E

(k)x are defined in the

following.

1) Transmission event T(k)x : this event occurs when a

legitimate transmitter in level k at x has a GN in levelk − 1, i.e., x ∈ Tk−1 where Tk−1 is given by (20).

2) Collision event C(k)x : this event occurs when a legitimate

node in level k at x transmits using the communicationresources that are also used by other legitimate nodes ina bounded space A, i.e., x ∈ Ck where

Ck ={x ∈ �d : |Zk(x)| �= 0

}(26)

with Zk(x) denoting the random set of all other nodesin level k using the same resources as the node at x.

3) Successful reception event R(k)x : this event occurs when

the SNR ζ(k)� received by the GN in level k − 1 from

its associated legitimate transmitter in level k at x isgreater than a threshold value ζ�,9 i.e., x ∈ Rk−1 where

Rk−1 ={x ∈ �d : ζ

(k)� > ζ�

}. (27)

4) Eavesdropping event E(k)x : this event occurs when the

SNR ζ(k)e received by at least one eavesdropping node,

from a legitimate transmitter in level k at x, is greaterthan a threshold value ζe, i.e., x ∈ Ek where

Ek =

{x ∈ �d : max

Xe∈Π(k)e

ζ(k)e > ζe

}. (28)

We consider that legitimate transmitters do not have channelknowledge for legitimate and eavesdropping links. The SNRthreshold values ζ� and ζe are set to provide secrecy rate Rs

when the event in (25) is true, where

Rs = [R� −W log2(1 + ζe

)]+ (29)

and R� ≤ W log2(1 + ζ�

). Since Rs ≤ R�, the fraction

Rs/R� bits can be transmitted confidentially, translating tobs ∈ [0, bg] transmitted confidential bits per node per round[cbits/node/round].

The DNS is achieved when inter-level network secrecyis obtained in all levels, that is, data transmitted withoutcollision are received successfully without being successfullyeavesdropped in all levels. With this observation, we defineDNS in the following.

9The required SNR depends on employed signaling constellation anddiversity method [58].


Definition 2 (Distributed network secrecy): For a node inlevel l at x communicating to a monitor, the DNS is achievedwhen the event

∧lk=1S

(k)x (30)

is true, where S(k)x is defined in (25). When l = L full DNS

is achieved.Remark 2: Data from a node in level l are transmitted

l times over different inter-level communication resourcesto reach the monitor. This multi-hop transmission may givemalicious nodes multiple opportunities for eavesdropping.On the other hand, multi-hop transmission may reduce theamount of energy required to communicate with the monitor.Therefore, the operating parameters (e.g., nodes density andtransmitted energy) in each level of the self-organized MWNdetermine the relationship between the DNS and the networklifetime.

We now define a metric to characterize the DNS in anMWN.

Definition 3 (DNS throughput): In an MWN with L levels,the DNS throughput is defined as

ρds �bs

λ� |A| EΠ�,Πe

⎧⎪⎨⎪⎩

L∑l=1

∑X∈Π

(l)� ∩A

l∏k=1

�Sk

(ϕ(l)k (X)

)⎫⎪⎬⎪⎭(31)

where10

ϕ(l)k (x) =

{x, for k = l

(G ◦ ϕ(l)k+1)(x), for k = l − 1, l − 2, · · · , 1

is the node in level l at x for k = l and its GN at level k fork < l, and

Sk = Tk−1 ∩ Ck ∩Rk−1 ∩ Ek

is the random set of all positions from which nodes in levelk transmit without collision, with successful reception, andwithout being successfully eavesdropped.

Remark 3: The product of indicator functions in (31)accounts for secure transmission of bs bits from level l to level1 in a round. Therefore, the DNS throughput measures theaverage number of bits that a node communicates with DNSin a round, and its unit is cbits/node/round. One can also definevariants of the DNS throughput starting from ρds in (31), forexample, λ�ρds denotes the throughput in cbits/m2/round.

Example 1: In the case of a two-level network, (31) withL = 2 becomes

ρds =bs

λ� |A| EΠ�,Πe

⎧⎪⎨⎪⎩

∑X∈Π

(1)� ∩A

�S1(X) (32)

+∑

X∈Π(2)� ∩A

�S2(X)�S1(G(X))

⎫⎪⎬⎪⎭ .

10Notation (f ◦ g)(x) stands for composition f(g(x)).

IV. DISTRIBUTED NETWORK SECRECY ANALYSIS

In this section, we first analyze the DNS throughput forvarious network configurations in generic fading channels, andthen derive its closed-form expressions in Nakagami-m fadingchannels.

A. Generic Fading Channels

Theorem 1 (DNS throughput in generic fading): The DNSthroughput of an MWN with L levels is given by

ρds = bs

L∑l=1

β(l)l∏

k=1

p(k)t p

(k)c p(k)r p

(k)e (33)

with

p(k)t = 1− exp

{−λ

(k−1)� B (rk)

}(34)

p(k)c = E

Π(k)�

{�Ck

(ϕ(l)k (x)

)}(35)

p(k)r = Fζ(k)�

(ζ�)

(36)

p(k)e = exp

{−λ(k)

e

∫�d

Fζ(k)e |dx,ω

(ζe)dω

}(37)

where, for a transmitter in level k, p(k)t is the transmission

probability, p(k)c is the probability of no collision, p(k)r is theprobability of successful reception, and p

(k)e is the probability

of unsuccesful eavesdropping.Proof: For a transmitter in level k, the random sets Tk−1

and Rk−1 depend on Π(k−1)� , Ck depends on Π

(k)� , and Ek

depends on Π(k)e . Therefore,

EΠ�,Πe

{L∑

l=1

∑X∈Π

(l)� ∩A

l∏k=1

�Sk

(ϕ(l)k (X)

)}(38)

=L∑

l=1

EΠ

(l)�

{ ∑X∈Π

(l)�

∩A

�Cl

(ϕ(l)l (X)

)

× E⋃l−1k=1 Π

(k)� ,Πe

{ l−1∏k=1

�Ck

(ϕ(l)k (X)

)

×l∏

k=1

�Tk−1

(ϕ(l)k (X)

)�Rk−1

(ϕ(l)k (X)

)�Ek

(ϕ(l)k (X)

)}}.

Note that Tk−1 depends on the presence of at least one node inlevel k−1 within a distance rk from ϕ

(l)k (x), Rk−1 depends on

the distance between ϕ(l)k (x) and ϕ

(l)k−1(x), and Ck−1 depends

on the number of level k − 1 nodes, each transmitting toits associated GN according to a communication protocol.Therefore, the right side of (38) can be written as11

L∑l=1

EΠ

(l)�

{ ∑X∈Π

(l)� ∩A

�Cl

(ϕ(l)l (X)

)}

×l∏

k=1

p(k)t p(k)r p

(k)e

l−1∏k=1

p(k)c . (39)

11For the case where all eavesdropping nodes aim to intercept legitimatetransmissions at each level, care must be taken to evaluate the expectation of∏l

k=1 �Ek

(ϕ(l)k (X)

).


ρds = bs

L∑l=1

β(l)

⎧⎨⎩

l∏k=1

p(k)c

[1− e−λ

(k−1)� πr2k

](E(k)b R� G0

ζ�N0W

)2/α2

αr2k

m−1∑t=0

1

t!γ

(2

α+ t,

ζ�N0Wrαk

E(k)b R�G0

)

× exp

⎧⎨⎩−2πλ

(k)e

α

(E

(k)b R�G0

ζeN0W

)2/α m−1∑t=0

1

t!Γ

(2

α+ t

)⎫⎬⎭⎫⎬⎭ (42)

The p(k)c is the probability that a node in level k transmits

without collision and can be written as (35).12 The p(k)t is the

probability that a node in level k transmits to a GN and canbe written as (18). The p

(k)r is the probability that a GN in

level k − 1 successfully receives data transmitted by a nodein level k, and can be written as p

(k)r = P {x ∈ Rk−1}. From

(27), we have

p(k)r = EDx,G(x)

{Fζ(k)� |Dx,G(x)

(ζ�)}

which results in (36). Finally, p(k)e is the probability that a nodein level k transmits without being successfully eavesdroppedand can be written as p

(k)e = P

{x ∈ Ek

}. From (28) and the

stationarity of Πe, we have

p(k)e = E

Π(k)e

{P

{max

Xe∈Π(k)e

ζ(k)�|Dx,Xe

≤ ζe

}}

= EΠ

(k)e

⎧⎨⎩

∏Xe∈Π

(k)e

[1− F

ζ(k)

�|Dx,Xe

(ζe)]⎫⎬⎭ . (40)

By using the probability generating functional of a PPP, weobtain (37).13 Recall that the collision event of a node in levelk at x depends on the communication resources utilized bythe other nodes in level k. It follows that the random set Ckdepends on the process Π

(k)� \{x}. Therefore, by using the

reduced Campbell formula [59], we can write the expectationin (39) as

EΠ

(l)�

{ ∑X∈Π

(l)� ∩A

�Cl

(ϕ(l)l (X)

)}

= λ(l)�

∫AEΠ

(l)�

{�Cl

(ϕ(l)l (ω)

)}dω

= λ(l)� p

(l)c |A| . (41)

Therefore, by substituting (41) into (39) and using (31), theDNS throughput results in (33).

Remark 4: Theorem 1 enables the evaluation of the DNSthroughput for MWNs as a function of the CCDF of receivedSNRs, node spatial distribution, multilevel cluster formation,propagation medium, and communication protocol.

12Closed form expressions can be obtained depending on the communica-tion protocol.

13Let ν(x) be a bounded measurable function of x ∈ �d . The generatingfunctional of a point process Π is G(ν) = EΠ

{∏X∈Π ν(X)

}. By

Campbell’s theorem [53], it is equal to

G(ν) = exp

{−∫�d

(1− ν(x))Λ(dx)

}

for a PPP with the spatial density Λ(x).

B. Nakagami-m Fading Channels

We now derive the closed-form expression for the DNSthroughput in Nakagami-m fading channels.

Theorem 2 (DNS throughput for Nakagami-m fading): TheDNS throughput in Nakagami-m fading channels is given by(42), shown at the top of this page, for positive integer m.

Proof: The DNS throughput is obtained from Theorem1 by determining the CCDF of the SNR in (36) and (37)for Nakagami-m fading channels. Using (12), the CCDF ofthe SNR received by a node at Y ∈ Πv conditioned on thedistance D from a transmitter in level k at x is

Fζ(k)

v|D(ξ) = F|H|2

(ξN0WD

α

E(k)b R�G0

).

Therefore,

Fζ(k)

v|D(ξ)=

m−1∑t=0

1

t!

(ξN0WD

α

E(k)b R�G0

)t

exp

{− ξN0WD

α

E(k)b R�G0

}(43)

for Nakagami-m fading channels [60]. Since the squared dis-tances are uniformly distributed between 0 and r2k, the CCDFof the received SNR averaged over the distance distributionresults in

p(k)r =2

r2k

m−1∑t=0

1

t!

(ξN0W

E(k)b R�G0

)t

(44)

×∫ rk

0

yαt+1 exp

{− ξN0Wyα

E(k)b R�G0

}dy

=2

αr2k

(E

(k)b R�G0

ξN0W

)2/α m−1∑t=0

1

t!γ

(2

α+ t,

ξN0Wrαk

E(k)b R�G0

).

For the eavesdropping network, substituting (43) into (37),the probability of unsuccessful eavesdropping in level k =L,L− 1, · · · , 1 becomes

p(k)e = exp

⎧⎨⎩−2πλ(k)

e

m−1∑t=0

1

t!

(ζeN0W

E(k)b R�G0

)t

×∫ ∞

0

y1+αt exp

{− ζeN0Wyα

E(k)b R�G0

}dy

}

= exp

⎧⎨⎩−2πλ

(k)e

α

(E

(k)b R�G0

ζeN0W

)2/α m−1∑t=0

1

t!Γ

(2

α+ t

)⎫⎬⎭(45)

where Γ(·) is the Gamma function [54]. Finally, (33), (34),(35), (44), and (45) give the closed-form expression (42)for the DNS throughput of an MWN in Nakagami-m fadingchannels.


V. CASE STUDY

We consider a case study with two-level wireless networks,for which we quantify both the DNS and the network lifetime.First, we describe the scenario and then provide the results interms of DNS throughput and average number of rounds pernode. The analysis is corroborated by simulation results forvarious network configurations.

A. Network Scenario and Performance Analysis

1) Network Scenario: We consider a scenario with a two-level (L = 2) legitimate network in R

2, composed of non-GNs in level 2 and GNs in level 1. A two-level eavesdrop-ping network is composed of eavesdropping nodes aiming tointercept information of non-GNs and GNs in levels 2 and1, respectively, with spatial density λ

(2)e = λ

(1)e = λe. We

consider ZT channels available to transmitting nodes in abounded space Bo(r) with area B (r) = πr2. Among the ZTchannels, Z2 = δ2ZT = (1− δ1)ZT with δ1 ∈ (0, 1) andZ1 = δ1ZT channels are available to legitimate nodes in level2 and 1, respectively.

2) Distributed Network Secrecy: The DNS throughput inNakagami-m fading channels depends on p

(l)c , determined

by the MAC protocol, according to (42). In particular, weconsider an access protocol according to which each le-gitimate node randomly selects a communication channelindependently of other legitimate nodes in the same level [5].Conditioned on the number nl of transmitting nodes in level l,the probability that a node in level l transmits without collisionis given by [61]

p(l)c (nl) =

(1− 1

Zl

)nl−1

. (46)

Therefore, the probability that a node in level l transmitswithout collision becomes

p(l)c = Enl

{p(l)c (nl)

}

=Zle

−N(l)t /Zl − e−N

(l)t

Zl − 1(47)

where N(l)t is the average number of level l transmitting nodes

in Bo(r) as

N(l)t = πr2 p

(l)t β(l)λ� . (48)

By using (47) and (48) in (42), we obtain the DNS throughputfor Nakagami-m fading channels.

3) Network Lifetime: In each round, every node generatesbg bits to communicate its observation. For a given R� =W log2

(1 + ζ�

), each non-GN transmits s2 = bg/ (R�T )

symbols per round. Thus, a typical GN transmits (n2 + 1)s2symbols where n2 is the number of non-GNs in a clusterwhose transmission to the GN is successfully received withoutcollision. The mean of n2 is given by

E {n2} = πr22 p(2)ga p(2)r p

(2)c β(2)λ� . (49)

TABLE IIPARAMETER VALUES IF NOT OTHERWISE SPECIFIED

Parameters Values Parameters Values

α 4 λ� 10−3

m 1 λe 3× 10−6

WT 1 β(1) 0.4

r1, r [m] 100 E(2)b [J] 10−6

r2 [m] 30 Echarged [J] 10

bg 2 Δ1 30

bs 1 δ1 0.7

From (7) and (49), the average number of transmitted symbolsper GN in a round results in

s1 = s2 En2{n2 + 1}

=bg

R�T

[β(2)

β(1)p(2)r p

(2)c

(1− e−πr22 β(1)λ�

)+ 1

]. (50)

Finally, by substituting (50) together with the expression fors2 into (24), we obtain the network lifetime for a two-levelwireless network as

Nround =Echarged

[E

(2)b bg

[β(2)p

(2)t +Δ1β

(1)p(1)t (51)

×(β(2)

β(1)p(2)r p

(2)c

(1− e−πr22 β(1)λ�

)+ 1

)]]−1

.

B. Performance Evaluation

We now evaluate the performance of a two-level wirelessnetwork described in Sec. V-A. Unless otherwise specified, thevalues of network parameters presented in Table II are used.14

1) Distributed network secrecy: Figure 2 shows ρds as afunction of E

(2)b for different values of Δ1 and ZT (ideal

MAC refers to the case with no collision). Simulation results,depicted by circles, show a good agreement with the analysis.It can be seen that ρds increases with E

(2)b up to a maximum

value, after which it decreases. This can be attributed to thecompeting effects of increasing E

(2)b , which increases the

legitimate reception capability as well as the eavesdroppingcapability. Note also that ρds increases with ZT since collisionsamong nodes are less frequent with more available channels. Itcan also be observed from Fig. 2 that increasing Δ1 increasesρds when E

(2)b is small, whereas the trend is opposite when

E(2)b is large. This behavior is further investigated in the next

figure.Figure 3 displays the contour of ρds as a function of

E(2)b and Δ1. It can be seen that the optimal value of Δ1,

which maximizes ρds, decreases as E(2)b increases. This can

be attributed to the fact that, when E(2)b is high, increasing the

transmitted energy at GNs increases the eavesdropping capa-bility more than the legitimate successful reception capability.Therefore, the joint optimization of parameters (e.g., energyratio and transmitted bit energy) is important for designing

14For the considered parameters, ρds can be thought of as the fraction of bsconfidential bits that each node successfully transmits with DNS per round.


Δ1 = 20, ideal MACΔ1 = 30, ideal MACΔ1 = 40, ideal MACΔ1 = 30, ZT = 7× 102

Δ1 = 30, ZT = 5× 102

ρds

[cbi

ts/n

ode/

roun

d]

E(2)b [J]

00.4

0.5

0.6

1 2 3 4

× 10−6

Fig. 2. ρds as a function of E(2)b for different values of energy ratio Δ1 and

number of available channels ZT. Circle markers are for simulation results.

ρds

[cbits/node/round]

Δ1

E(2)b [J]

1 2 3 4

× 10−6

10

14

18

22

26

30

0.46

0.47

0.48

0.49

0.50

Fig. 3. ρds as a function of E(2)b and Δ1.

MWNs with DNS. For instance, the maximum ρds is achievedwith E

(2)b = 1.6 μJ and Δ1 = 24.

Figure 4 shows ρds as a function of E(2)b for different

values of λe with no collision. Simulation results, depictedby circles, show a good agreement with the analysis. It canbe seen that, in the absence of eavesdroppers (λe = 0), ρds

increases with E(2)b as expected since legitimate reception ca-

pability increases with E(2)b . In the presence of eavesdroppers,

increasing E(2)b above a certain value is harmful since the

increase in eavesdropping capability outweigh the increase inthe legitimate reception capability especially for large λe.

Figure 5 displays the contour of ρds as a function of λe andλ�. It can be seen that ρds increases with λ� for a given λe. Thiscan be attributed to the fact that the legitimate transmissioncapability, from non-GN to its associated GN, increases withλ�. The increase in ρds is more significant for smaller values ofλe, where legitimate transmission capability heavily outweigh

λe = 0

λe = 1× 10−6

λe = 5× 10−6

λe = 1× 10−5

λe = 5× 10−5

λe = 1× 10−4

ρds

[cbi

ts/n

ode/

roun

d]

E(2)b [J]

0.00

0.2

0.4

0.6

0.8

1 2 3 4

× 10−6

Fig. 4. ρds as a function of E(2)b for different values of eavesdropping node

density λe. Circle markers are for simulation results.

ρds

[cbits/node/round]

λ�

[nod

es/m

2]

λe [nodes/m2]

0

0.4

0.6

0.8

1

1

2

2

3

3

4

4

× 10

× 10−6

-3

5

5

Fig. 5. ρds as a function of λe and λ�.

the eavesdropping capability.2) Network lifetime: Figure 6 shows Nround as a function of

δ1 for different ZT. It can be seen that Nround increases with δ1.This can be attributed to the fact that the energy consumptiondepends on both transmissions and collisions at level 2, andnot on the collisions at level 1. In fact, smaller Z2 (higherδ1) induces more frequent collisions among non-GNs, andconsequently a smaller amount of information is received fromnon-GNs, which reduces the energy consumption of GNs.

Figure 7 displays the contour of Nround as a function of E(2)b

and Δ1. It can be seen that Nround becomes smaller as E(2)b or

Δ1 increases due to higher energy consumption at each node.By comparing Figs. 3 and 7, it is evident that the optimalvalues of E

(2)b and Δ1 that maximize ρds do not maximize

Nround. Therefore, it is important to jointly consider ρds andNround in designing energy-efficient MWNs with DNS. Therelationship between ρds and Nround is now explored.


ZT = 200

ZT = 400

ZT = 100

ZT = 50

Nro

und

[rou

nds]

δ1

0.0 0.2 0.4 0.6 0.8 1.02.0

3.0

2.2

2.4

2.6

2.8

× 105

Fig. 6. Nround as a function of δ1 for different number of total availablechannels ZT.

N

round[rounds]

Δ1

E(2)b

1

2

2 3

4

4

× 10

× 10−6

5

6

10

14

18

22

26

30

Fig. 7. Nround as a function of E(2)b and Δ1.

3) Relationship between DNS and network lifetime: Fig-ure 8 shows the relationship between ρds and Nround fordifferent values of E(2)

b and λe. Simulation results, depicted bycircles, show a good agreement with the analysis. For a givenE

(2)b , it can be seen that ρds decreases as λe increases, while

Nround is not affected by λe. In the absence of eavesdroppingnodes (λe = 0), a trade-off between ρds and Nround exists sinceρds increases while Nround decreases with increasing E

(2)b . This

relationship changes in the presence of eavesdropping nodes(λe > 0) especially for large λe such as λe = 10−5 whereboth ρds and Nround decrease as E

(2)b increases.

Figure 9 shows ρds as a function of Nround for differentvalues of ZT and δ1. It can be seen that ρds increases andthen, after a certain point, decreases while Nround alwaysincreases as δ1 increases. Therefore, a trade-off betweenρds and Nround exists for large values of δ1, whereas theyboth follow the same trend for small values of δ1. This

λe = 0

λe = 1× 10−6

λe = 3× 10−6

λe = 5× 10−6

λe = 1× 10−5

Increasing E(2)b

E(2)b = [0.53, · · · , 6] μJ

Nround [rounds]

ρds

[cbi

ts/n

ode/

roun

d]

0.00

0.2

0.4

0.6

0.8

1 2 3 4

× 105

Fig. 8. ρds as a function of Nround for different values of λe and E(2)b . Circle

markers are for simulation results.

ZT = 200

ZT = 400

ZT = 100

ZT = 50

δ1 = [0.02, · · · , 0.98]Increasing δ1

Nround [rounds]

ρds

[cbi

ts/n

ode/

roun

d]

0.0

0.2

0.4

0.6

2.0

× 1052.4 2.6 2.8 3.02.2

Fig. 9. ρds as a function of Nround for different values of ZT and δ1.

behavior of ρds can be attributed to competing effects ofincreasing δ1, which increases the capability of transmissionwithout collision as well as the capability of eavesdroppingthe confidential information in level 1. In fact, collisions inlevel 1 reduce ρds more than collisions in level 2, since eachGN transmits (n2 + 1)bs cbits while each non-GN transmitsbs cbits. On the other hand, collisions in level 2 reduce theamount of information transmitted and, therefore, the amountof information eavesdropped in level 1.

We now evaluate the achievable DNS throughput during thenetwork lifetime, that is ρds ×Nround, to measure the averagenumber of confidential bits communicated per node during thenetwork lifetime. Figure 10 shows ρds×Nround as a function ofE

(2)b and Δ1. From this figure, it can be observed that lower

Δ1 achieves higher ρds×Nround for all values of E(2)b , whereas

from Fig. 3, lower Δ1 does not necessarily achieve higher ρds

for varying E(2)b .


Δ1

E(2)b [J]

ρds ×

Nround

[cbits/node]1

1

2

2 3 4

× 10

× 10−6

5

10

14

18

22

26

30

Fig. 10. ρds ×Nround as a function of E(2)b and Δ1.

VI. CONCLUSION

This paper introduces the concept of DNS and establishes afoundation for the network secrecy in self-organizing MWNsaccounting for node spatial distribution, multilevel clusterformation, propagation medium, communication protocol, andenergy consumption. By quantifying the DNS throughput andthe energy consumption, we showed how network config-urations influence both the DNS and the network lifetime.Specifically, our results demonstrate that different configu-rations of transmitted energy and communication resourcesinduce different relationships between the DNS throughputand the network lifetime. The outcomes of our work provideguidelines for the design and analysis of reliable and energy-efficient self-organizing MWNs with DNS.

ACKNOWLEDGMENT

The authors wish to thank and W. Dai, Y. Shen, and T. Wangfor the careful reading of the manuscript.

REFERENCES

[1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “A surveyon sensor networks,” IEEE Commun. Mag., vol. 40, no. 8, pp. 102–114,Aug. 2002.

[2] M. Tubaishat and S. Madria, “Sensor networks: an overview,” IEEEPotentials, vol. 22, no. 2, pp. 20–23, Apr./May 2003.

[3] D. Estrin, L. Girod, G. Pottie, and M. Srivastava, “Instrumentingthe world with wireless sensor networks,” in Proc. IEEE Int. Conf.Acoustics, Speech, and Signal Processing, vol. 4, Salt Lake City, UT,May 2001, pp. 2033–2036.

[4] S. Simic and S. Sastry, “Distributed environmental monitoring usingrandom sensor networks,” in Proc. Workshop Information Processing inSensor Networks. Springer, Paolo Alto, CA, Apr. 2003, pp. 582–592.

[5] D. Dardari, A. Conti, C. Buratti, and R. Verdone, “Mathematicalevaluation of environmental monitoring estimation error through energy-efficient wireless sensor networks,” IEEE Trans. Mobile Comput., vol. 6,no. 7, pp. 790–802, Jul. 2007.

[6] C. E. Shannon, “Communication theory of secrecy systems,” Bell SystemTechnical J., vol. 28, no. 4, pp. 656–715, Oct. 1949.

[7] A. D. Wyner, “The Wire-Tap Channel,” Bell System Technical J., vol. 54,no. 8, pp. 1355–1387, Oct. 1975.

[8] A. B. Carleial and M. E. Hellman, “A note on Wyner’s wiretap channel,”IEEE Trans. Inf. Theory, vol. 23, no. 3, pp. 387–390, May 1977.

[9] S. Leung-Yan-Cheong and M. Hellman, “The Gaussian wire-tap chan-nel,” IEEE Trans. Inf. Theory, vol. 24, no. 4, pp. 451–456, Jul. 1978.

[10] I. Csiszar and J. Korner, “Broadcast channels with confidential mes-sages,” IEEE Trans. Inf. Theory, vol. 24, no. 3, pp. 339–348, May 1978.

[11] Y. Liang, H. V. Poor, and S. Shamai, “Secure communication over fadingchannels,” IEEE Trans. Inf. Theory, vol. 54, no. 6, pp. 2470–2492, Jun.2008.

[12] X. Zhou, M. R. McKay, B. Maham, and A. Hjørungnes, “Rethinking thesecrecy outage formulation: A secure transmission design perspective,”IEEE Commun. Lett., vol. 15, no. 3, pp. 302–304, Mar. 2011.

[13] X. Zhou, R. K. Ganti, J. G. Andrews, and A. Hjørungnes, “On thethroughput cost of physical layer security in decentralized wirelessnetworks,” IEEE Trans. Wireless Commun., vol. 10, no. 8, pp. 2764–2775, Aug. 2011.

[14] Y. Liang and H. V. Poor, “Multiple-access channels with confidentialmessages,” IEEE Trans. Inf. Theory, vol. 54, no. 3, pp. 976–1002, Mar.2008.

[15] Y. Liang, H. V. Poor, and L. Ying, “Secrecy throughput of MANETsunder passive and active attacks,” IEEE Trans. Inf. Theory, vol. 57,no. 10, pp. 6692–6702, Oct. 2011.

[16] E. Tekin and A. Yener, “The Gaussian multiple access wire-tap channel,”IEEE Trans. Inf. Theory, vol. 54, no. 12, pp. 5747–5755, Dec. 2008.

[17] Y. Liang, A. Somekh-Baruch, H. V. Poor, S. Shamai, and S. Verdu,“Capacity of cognitive interference channels with and without secrecy,”IEEE Trans. Inf. Theory, vol. 55, no. 2, pp. 604–619, Feb. 2009.

[18] Z. Han, N. Marina, M. Debbah, and A. Hjørungnes, “Physical layersecurity game: interaction between source, eavesdropper, and friendlyjammer,” EURASIP Journal on Wireless Communications and Network-ing, vol. 2009, p. 1–10, Jan. 2010.

[19] S. Goel and R. Negi, “Guaranteeing secrecy using artificial noise,” IEEETrans. Wireless Commun., vol. 7, no. 6, pp. 2180–2189, Jun. 2008.

[20] , “Secret communication in presence of colluding eavesdroppers,”in Proc. Military Commun. Conf., Atlantic City, NJ, Oct. 2005, pp.1501–1506.

[21] P. C. Pinto, J. O. Barros, and M. Z. Win, “Secure communication instochastic wireless networks – Part II: Maximum rate and collusion,”IEEE Trans. Inf. Forens.Security, vol. 7, no. 1, pp. 139–147, Feb. 2012.

[22] O. Koyluoglu, C. Koksal, and H. El Gamal, “On secrecy capacity scalingin wireless networks,” IEEE Trans. Inf. Theory, vol. 58, no. 5, pp. 3000–3015, May 2012.

[23] A. Hero, “Secure space-time communication,” IEEE Trans. Inf. Theory,vol. 49, no. 12, pp. 3235–3249, Dec. 2003.

[24] F. Oggier and B. Hassibi, “The secrecy capacity of the MIMO wiretapchannel,” in Proc. IEEE Int. Symp. on Inf. Theory, Toronto, Canada, Jul.2008, pp. 524–528.

[25] A. Khisti and G. W. Wornell, “Secure transmission with multipleantennas I: the MISOME wiretap channel,” IEEE Trans. Inf. Theory,vol. 56, no. 7, pp. 3088–3104, Jul. 2010.

[26] R. Ahlswede and I. Csiszar, “Common randomness in informationtheory and cryptography - Part I: Secret sharing,” IEEE Trans. Inf.Theory, vol. 39, no. 4, pp. 1121–1132, Jul. 1993.

[27] U. Maurer, “Secret key agreement by public discussion from commoninformation,” IEEE Trans. Inf. Theory, vol. 39, no. 3, pp. 733–742, May1993.

[28] R. Wilson, D. Tse, and R. Scholtz, “Channel identification: Secretsharing using reciprocity in ultrawideband channels,” IEEE Trans. Inf.Forens. Security, vol. 2, no. 3, pp. 364–375, Sep. 2007.

[29] L. Lai, Y. Liang, and H. V. Poor, “A unified framework for keyagreement over wireless fading channels,” IEEE Trans. Inf. Forens.Security, vol. 7, no. 2, pp. 480–490, Apr. 2012.

[30] Y. Shen and M. Z. Win, “Intrinsic information of wideband channels,”IEEE J. Sel. Areas Commun., vol. 31, no. 9, Sep. 2013.

[31] L. Lai and H. El Gamal, “The relay–eavesdropper channel: Cooperationfor secrecy,” IEEE Trans. Inf. Theory, vol. 54, no. 9, pp. 4005–4019,Sep. 2008.

[32] W. Saad, Z. Han, T. Basar, M. Debbah, and A. Hjørungnes, “Distributedcoalition formation games for secure wireless transmission,” MobileNetworks and Applications, vol. 16, no. 2, pp. 231–245, Apr. 2011.

[33] H. Weingarten, T. Liu, S. Shamai, Y. Steinberg, and P. Viswanath,“The capacity region of the degraded multiple-input multiple-outputcompound broadcast channel,” IEEE Trans. Inf. Theory, vol. 55, no. 11,pp. 5011–5023, Nov. 2009.

[34] M. Z. Win, “A mathematical model for network interference,” IEEECommunication Theory Workshop, Sedona, AZ, May 2007.

[35] M. Z. Win, P. C. Pinto, and L. A. Shepp, “A mathematical theory ofnetwork interference and its applications,” Proc. IEEE, vol. 97, no. 2,pp. 205–230, Feb. 2009.


[36] M. Haenggi, J. G. Andrews, F. Baccelli, O. Dousse, andM. Franceschetti, “Stochastic geometry and random graphs forthe analysis and design of wireless network,” IEEE J. Sel. AreasCommun., vol. 27, no. 7, pp. 1029–1046, Sep. 2009.

[37] J. Orriss and S. K. Barton, “Probability distributions for the numberof radio transceivers which can communicate with one another,” IEEETrans. Commun., vol. 51, no. 4, pp. 676–681, Apr. 2003.

[38] E. Salbaroli and A. Zanella, “Interference analysis in a Poisson fieldof nodes of finite area,” IEEE Trans. Veh. Technol., vol. 58, no. 4, pp.1776–1783, May 2009.

[39] A. Rabbachin, T. Q. Quek, H. Shin, and M. Z. Win, “Cognitive networkinterference,” IEEE J. Sel. Areas Commun., vol. 29, no. 2, pp. 480–493,Feb. 2011.

[40] E. S. Sousa, “Performance of a spread spectrum packet radio networklink in a Poisson field of interferers,” IEEE Trans. Inf. Theory, vol. 38,no. 6, pp. 1743–1754, Nov. 1992.

[41] A. Ghasemi and E. S. Sousa, “Interference aggregation in spectrum-sensing cognitive wireless networks,” IEEE J. Sel. Topics Signal Pro-cess., vol. 2, no. 1, pp. 41–56, Feb. 2008.

[42] P. C. Pinto and M. Z. Win, “Communication in a Poisson field ofinterferers – Part I: Interference distribution and error probability,” IEEETrans. Wireless Commun., vol. 9, no. 7, pp. 2176–2186, Jul. 2010.

[43] , “Communication in a Poisson field of interferers – Part II: Channelcapacity and interference spectrum,” IEEE Trans. Wireless Commun.,vol. 9, no. 7, pp. 2187–2195, Jul. 2010.

[44] J. Ilow, D. Hatzinakos, and A. N. Venetsanopoulos, “Performance of FHSS radio networks with interference modeled as a mixture of Gaussianand alpha-stable noise,” IEEE Trans. Commun., vol. 46, no. 4, pp. 509–520, Apr. 1998.

[45] X. Yang and A. P. Petropulu, “Co-channel interference modeling andanalysis in a Poisson field of interferers in wireless communications,”IEEE Trans. Signal Process., vol. 51, no. 1, pp. 64–76, Jan. 2003.

[46] S. Govindasamy, D. W. Bliss, and D. H. Staelin, “Spectral efficiencyin single-hop ad-hoc wireless networks with interference using adaptiveantenna arrays,” IEEE J. Sel. Areas Commun., vol. 25, no. 7, pp. 1358–1369, Sep. 2007.

[47] J. Lee, J. G. Andrews, and D. Hong, “Spectrum-sharing transmissioncapacity,” IEEE Trans. Wireless Commun., vol. 10, no. 9, pp. 3053–3063, Sep. 2011.

[48] P. C. Pinto and M. Z. Win, “Percolation and connectivity in theintrinsically secure communications graph,” IEEE Trans. Inf. Theory,vol. 58, no. 3, pp. 1716–1730, Mar. 2012.

[49] M. Haenggi, “The secrecy graph and some of its properties,” in Proc.IEEE Int. Symp. on Inf. Theory, Toronto, Canada, Jul. 2008, pp. 539–543.

[50] X. Zhou, R. K. Ganti, and J. G. Andrews, “Secure wireless networkconnectivity with multi-antenna transmission,” IEEE Trans. WirelessCommun., vol. 10, no. 2, pp. 425–430, Feb. 2011.

[51] A. Rabbachin, A. Conti, and M. Z. Win, “The role of aggregateinterference on intrinsic network secrecy,” in Proc. IEEE Int. Conf.Commun., Ottawa, Canada, Jun. 2012, pp. 3548–3553.

[52] J. Lee, H. Shin, and M. Z. Win, “Secure node packing of large-scalewireless networks,” in Proc. IEEE Int. Conf. Commun., Ottawa, Canada,Jun. 2012, pp. 815–819.

[53] J. F. Kingman, Poisson Processes. Oxford University Press, 1993.[54] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.

Dover Publications, 1970.[55] J. Gil-Pelaez, “Note on the inversion theorem,” Biometrika, vol. 38, no.

3/4, pp. 481–482, Dec. 1951.[56] R. Verdone, D. Dardari, G. Mazzini, and A. Conti, Wireless Sensor and

Actuator Networks: Technologies, Analysis and Design. Elsevier, 2008.[57] F. Zhao, J. Liu, J. Liu, L. Guibas, and J. Reich, “Collaborative signal

and information processing: an information–directed approach,” Proc.IEEE, vol. 91, no. 8, pp. 1199–1209, Aug. 2003.

[58] A. Conti, W. M. Gifford, M. Z. Win, and M. Chiani, “Optimized simplebounds for diversity systems,” IEEE Trans. Commun., vol. 57, no. 9, pp.2674–2685, Sep. 2009.

[59] F. Baccelli and B. Błaszczyszyn, Stochastic Geometry and Wireless Net-works, Volume I — Theory, ser. Foundations and Trends in Networking.NoW Publishers, 2009.

[60] M. K. Simon and M.-S. Alouini, Digital Communication over FadingChannels. Wiley-IEEE Press, 2004.

[61] Leon-Garcia and I. Widjaja, Communication Networks: FundamentalConcepts and Key Architectures. McGraw-Hill, 2000.

Jemin Lee (S’06-M’11) is a Postdoctoral Fellowat the Massachusetts Institute of Technology since2010 and a Research Fellow at Singapore Universityof Technology and Design since 2013. Her researchinterests involve communication theory and stochas-tic geometry applied to cognitive radio networks,heterogeneous wireless networks, and network se-crecy. Dr. Lee is a Guest Editor for the ELSEVIERPhysical Communication and in the organization ofnumerous international conferences. She has beenrecognized as an exemplary reviewer of the IEEE

Communication Letters. She received the Chun-Gang Outstanding ResearchAward and fellowship from National Research Foundation of Korea.

Andrea Conti (S’99-M’01-SM’11) is a Profes-sore Aggregato at the University of Ferrara. Healso holds Research Affiliate appointments at IEIIT,Consiglio Nazionale delle Ricerche, and at LIDS,Massachusetts Institute of Technology. His researchinterests involve theory and experimentation of wire-less systems and networks including network local-ization, adaptive diversity communications, cooper-ative relaying techniques, and network secrecy. Dr.Conti is serving as an Editor for the IEEE Commu-nications Letters and served as an Associate Editor

for the IEEE Transactions on Wireless Communications. He is elected Chairof the IEEE Communications Society’s Radio Communications TechnicalCommittee and is an IEEE Distinguished Lecturer. He is a recipient of theHTE Puskas Tivadar Medal and is co-recipient of the IEEE CommunicationsSociety’s Fred W. Ellersick Prize and of the IEEE Communications Society’sStephen O. Rice Prize in the Field of Communications Theory.

Alberto Rabbachin (S’03-M’07) is a PostdoctoralFellow at the Massachusetts Institute of Technology.His research interests involve communication theoryand stochastic geometry applied to real-problemsin wireless networks including network secrecy,cognitive radio, ultrawide band transceiver design,network synchronization, ranging techniques, andinterference exploitation. Dr. Rabbachin serves asan Editor for the IEEE Communications Lettersand in the organization of numerous internationalconferences. He received the International Outgoing

Marie Curie Fellowship, the Nokia Fellowship, the European CommissionJRC best young scientist award, and the IEEE William R. Bennett Prize inthe Field of Communications Networking.

Moe Z. Win (S’85-M’87-SM’97-F’04) is a Pro-fessor at the Massachusetts Institute of Technology(MIT) and the founding director of the WirelessCommunication and Network Sciences Laboratory.Prior to joining MIT, he was with AT&T ResearchLaboratories and with the Jet Propulsion Laboratory.His research encompasses developing fundamen-tal theories, designing algorithms, and conductingexperimentation for a broad range of real-worldproblems. Dr. Win is a Fellow of the AAAS andof the IEEE. He is an elected Member-at-Large on

the IEEE Communications Society Board of Governors. He served as Editorfor various IEEE journals and chaired a number of international conferences.He received the Fulbright Fellowship, the Copernicus Fellowship, and theLaurea Honoris Causa from the University of Ferrara. Together with studentsand colleagues, his papers have received several awards including the IEEECommunications Societys Stephen O. Rice Prize, the IEEE Aerospace andElectronic Systems Societys M. Barry Carlton Award, and the IEEE Antennasand Propagation Societys Sergei A. Schelkunoff Transactions Prize PaperAward. He was honored with the IEEE Kiyo Tomiyasu Award and the IEEEEric E. Sumner Award.

ieee journal on selected areas in communications, … · 2018-05-17 · ieee journal on selected...

Documents